Mechanobiology of Biofilms

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Page 2 of 3

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Linear Transformations: Injective and Surjective

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Matrix Operations: Transposition, Rank, and Basis Change

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Matrix Properties

Explores matrix shapes, compatibility, and invertibility, including staggered shapes and system compatibility.

Determinants and Properties

Covers the definition and properties of determinants, including the rule of Sarrus for 3x3 matrices.

Matrix Form and IO Analysis

Covers Material Flow Analysis in matrix form and Input-Output Analysis, exploring balance equations, transfer coefficients, GHG emissions, and economic impact.

Matrix Operations: Product and Inverse

Covers matrix operations, focusing on the product and inverse of matrices.

Matrix Operations: Definitions and Examples

Covers the basic operations on matrices, including addition, scalar multiplication, and matrix multiplication.

Projections and Applications

Explores projections in R³, matrix properties, and trace concepts with practical examples.